Knowledge transitions in document-grounded dialogs can be divided into two types namely, transition across different documents (out-topic) and within the same document (intra-topic). Transitions across different documents occur between topic vertices in our Coref-MDG and usually requires multi-hop reasoning. We use the residual graph propagation (Step II in Figure REF ) to model such transitions in Coref-MDG. Specifically, we devise a variant of Relational Graph Attention Layer(RGAT) [1]} layer with concatenated residual connection [2]}, named Res-RGAT. This layer facilitates the deeper multi-hop information propagation by avoiding information loss and the over-smooth problem [3]}. The output \(\mathbf {H^{out}} \in \mathbb {R}^{|\mathcal {G}| \times d_{out}}\)  of one Res-RGAT is the concatenation of the propagated results and the input \(\mathbf {H^{in}} \in \mathbb {R}^{|\mathcal {G}| \times d_{in}}\) , which is formulated as:
\(\mathbf {H^{out}} = W[\mathbf {H^{in}}, \textsc {RGAT}(\mathbf {H^{in}}, \mathbf {R}, \mathcal {E}, \mathcal {G})]\\\) 
